A substantial portion of the circuit-board space of conventional radios (e.g., in cellular phones, etc.) is occupied by off-chip components (e.g., inductors, capacitors, etc.). If all of the components of the radio could be incorporated onto a single chip, the resulting radio would be substantially smaller and more energy efficient than existing radios. To this end, investigators are studying how to create a “single-chip” radio.
Some proposed architectures for the single-chip radio (and interim architectures) include subsystems that incorporate micro-electromechanical systems (“MEMS”) technology. Examples of radio subsystems or “micromechanical circuits” that incorporate MEMS are switches (e.g., for transmit/receive selection; antenna selection, etc.), RF and IF filters, signal processors, and tunable oscillators. The MEMS devices that are used in these subsystems function as “circuit elements,” and include MEMS resonators, inductors and capacitors. The branch of MEMS technology pertaining to devices for RF applications, such as the single-chip radio, is referred to as “RF MEMS.”
Many of the more useful micromechanical circuits for RF communications are those that include high-Q resonators and microwave and millimeter-wave high-Q filters. As is well known, the “Q” or “quality factor” of a resonator or filter is a measure of its selectivity (among other accepted definitions).
Possessing a “high” Q is important in oscillators because adequate short- and long-term stability of oscillation frequency is assured only when the Q of the frequency-setting tank circuit exceeds a certain threshold. The ability to implement very selective IF and RF filters is also dependent upon high tank Q. See, e.g., Nguyen et al., “Frequency-Selective MEMS for Miniaturized Low-Power Communication Device,” IEEE Trans. Microwave Theory Tech., v(47), no.8, pp. 1486-1503 (August 1999).
MEMS-based resonators have been demonstrated at HF (3 MHz to 30 MHz), VHF (about 30 MHz to 300 MHz) and even UHF (300 MHz to 3 GHz). The challenge is to maintain an acceptably-high Q at these frequencies. Three types of prior-art MEMS resonators, which are capable of operating at HF or higher frequencies, are discussed below (see FIGS. 1 through 3).
FIG. 1 depicts “clamped-clamped beam” resonator 100, which consists of movable beam 102 and stationary drive electrode 108. Beam 102, which is electrically conductive, is anchored or “clamped” to underlying ground plane/sense electrode 106 at anchors 104. Electrode 108 is disposed beneath beam 102. The beam and electrode are separated by gap 110.
Resonator 100 accepts two electrical inputs, vi and vp. Electrical input vp is a DC-bias voltage that is applied to beam 102 via ground plane 106. This bias voltage generates an electrostatic force that statically bends or flexes beam 102 downward toward electrode 108, reducing the size of gap 110. It is typically necessary to reduce the size of gap 110 in this fashion since gap 110 is too large as formed to provide adequate electromagnetic coupling for most situations.
Electrical input vi is an ac excitation signal that is applied to electrode 108. The frequency of electrical input vi is swept, and, in response to certain frequencies, beam 102 vibrates. A current, io, is generated by the vibration of beam 102. This current, which is the output of resonator 100, is detected directly off the DC-biased ground plane/sense electrode 106.
A clamped-clamped resonator having a quality factor of about 8000 at 8.5 MHz resonant frequency (HF) has been demonstrated. See, e.g., Nguyen et al., “Transceiver Front-End Architectures Using Vibrating Micromechanical Signal Processors,” cited above.
Clamped-clamped resonators can be designed for resonant frequencies as high as the UHF range, as a function of material (e.g., polycrystalline silicone, diamond, etc.), vibration mode, and resonator beam dimensions. Furthermore, clamped-clamped resonators are readily fabricated with high stiffness, which is advantageous, because the stiffness of the resonator is proportional to the dynamic range of circuits that include these resonators.
But the utility of clamped-clamped resonators is limited. This limitation pertains not to operating frequency, but rather to an inability to maintain a suitably high quality factor as operating (resonant) frequency increases. In particular, due to the relatively high stiffness of most clamped-clamped resonator designs, a substantial portion of internal energy is dissipated through anchors 104 as the resonant frequency approaches the VHF range.
One solution to this problem is to further miniaturize the dimensions of a clamped-clamped resonator from micron-scale down to submicron or nano-scale. At these smaller dimensions, stiffness can be limited to smaller values to reduce energy loss (to the substrate) through the anchors. But this approach disadvantageously sacrifices power-handling capability or dynamic range, so that it might prove to be unworkable in certain situations, such as for communications applications in which co-site interference is a problem.
To retain a sufficiently high quality factor at VHF frequencies without sacrificing power-handling capability, a “free-free beam” resonator design was developed. FIG. 2 depicts an example of vertical-mode, free-free resonator 200.
Free-free resonator 200 includes movable beam 202 and stationary drive electrode 208. Beam 202, which is electrically conductive, is supported at its flexural nodal points 201 by four torsional-mode supports 203. The remote end (from beam 202) of each support 203 is anchored or “clamped” to underlying ground plane/sense electrode 206 at anchors 204. Electrode 208 is disposed beneath beam 202. Electrode 208 and beam 202 are separated by gap 210. Beam 202 is biased and excited to resonance in the same fashion as beam 102.
Supports 203 have a length that is one-quarter wavelength of the operating (resonant) frequency of resonator 200. This “quarter-wave” length causes an impedance transformation that advantageously isolates beam 202 from anchors 204. In other words, beam 202 ideally experiences zero mechanical impedance into its supports 203, effectively operating as if it were levitated without any supports. As such, the energy-dissipation mechanisms prevailing in clamped-clamped resonators like resonator 100 are substantially suppressed. Consequently, for a similarly-dimensioned resonant structure (i.e., the beam), free-free resonator 200 can attain a relatively higher Q than clamped-clamped resonator 100 at higher frequencies. See, e.g., U.S. Pat. No. 6,249,073; Wang et al., “VHF Free-Free Beam High-Q Micromechanical Resonators,” Technical Dig., Int'l IEEE Micro Electro Mechanical Systems Conf., Orlando, Fla., pp. 453-458 (Jan. 17-21, 1999). And since it is not necessary to reduce the size of beam 202 to address stiffness considerations (as for clamped-clamped resonator 100), free-free resonator 200 provides adequate dynamic range and power-handling capabilities.
Free-free resonators have been demonstrated at frequencies between 30-90 MHz (VHF) with a substantially constant Q that exceeds 8000. See, e.g., U.S. Pat. No. 6,249,073; and Wang et al., “VHF Free-Free Beam High-Q Micromechanical Resonators,” cited above.
While free-free resonator 200 advantageously provides high Q at high frequency, it does have some drawbacks. Some of the key drawbacks of this resonator are related to its vertical mode (i.e., “up and down”) of operation. In particular, as a vertical-mode resonator, free-free resonator 200 exhibits:                Topography-induced frequency uncertainty.        Lower Q due to larger energy dissipation through anchors 204.        Fabrication complexity issues that often constrain vertical mode resonators to be one-port devices, effectively eliminating opportunities for balanced or differential-mode operation.        Geometric inflexibility imposed by vertical-mode operation.        
The relatively long length of quarter-wave supports 203 is the cause of another drawback of (vertical-mode) resonator 200. Specifically, due to the relatively long length of quarter-wave supports 203, resonator 200 is susceptible to “pull-in” or “pull-down.” Pull-down is a phenomenon whereby the resonant structure (i.e., beam 202) is pulled into contact with an underlying structure (i.e., electrode 208) due to the applied DC-bias voltage. This contact prevents the resonant structure from vibrating. In the case of quarter-wave supports 203, the application of even a small DC-bias voltage, as is required across between beam 202 and electrode 208 to reduce gap 210 to an acceptably-small size, might cause pull-in.
To address the drawbacks of the vertical-mode resonator, a lateral-mode, free-free beam resonator was developed. See, e.g., Hsu et al., “Q-Optimized Lateral Free-Free Beam Micromechanical Resonators,” Dig. of Tech. Papers, 11th Int'l, Conf. on Solid State Sensors & Actuators (Transducers '01), Munich, Germany, pp. 1110-1113 (Jun. 10-14, 2001).
FIG. 3 depicts lateral-mode, free-free resonator 300. As depicted in FIG. 3, resonator 300 includes movable beam 302 and flanking stationary electrodes 308A and 308B. Electrode 308A is a drive electrode (i.e., causes beam 302 to vibrate) and electrode 308B is a sense electrode (i.e., senses vibration of beam 302). Each electrode 308 is separated from beam 302 by gap 310. Beam 302, which is electrically conductive, is supported at its nodal points 301 by four lateral-flexural-mode supports 303. The remote end (from beam 302) of each support 303 is anchored or “clamped” to underlying ground plane/sense electrode 306 at anchors 304.
Lateral-mode resonator 300 avoids some of the drawbacks of a vertical-mode resonator, as discussed above. The relatively long length of quarter-wave supports 303 does not render lateral-mode resonator 300 susceptible to pull-in since, under applied DC-bias, the direction of movement of beam 302 is horizontal, not vertical.
To investigate the degree of isolation provided by (second-mode) supports 303, the length of supports 303 was varied. Variations from the optimal length of supports 303 (quarter-wave) resulted in a drop in Q (e.g., to about 7000 for a decrease in the length of supports 303 from 25.4 microns to 5.6 microns and to about 4000 for an increase in the length of supports 303 from 25.4 microns to about 31 microns).
It is apparent, then, that each resonator described above has drawbacks that limit its utility. A need remains, therefore, for an improved resonator design.